3 * $Id: mpx-ksqr.c,v 1.6 2000/10/08 15:48:35 mdw Exp $
5 * Karatsuba-based squaring algorithm
7 * (c) 1999 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
14 * Catacomb is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU Library General Public License as
16 * published by the Free Software Foundation; either version 2 of the
17 * License, or (at your option) any later version.
19 * Catacomb is distributed in the hope that it will be useful,
20 * but WITHOUT ANY WARRANTY; without even the implied warranty of
21 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22 * GNU Library General Public License for more details.
24 * You should have received a copy of the GNU Library General Public
25 * License along with Catacomb; if not, write to the Free
26 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
30 /*----- Revision history --------------------------------------------------*
32 * $Log: mpx-ksqr.c,v $
33 * Revision 1.6 2000/10/08 15:48:35 mdw
34 * Rename Karatsuba constants now that we have @gfx_kmul@ too.
36 * Revision 1.5 2000/10/08 12:11:01 mdw
37 * Use @mpx_ueq@ instead of @MPX_UCMP@.
39 * Revision 1.4 2000/07/29 17:04:02 mdw
40 * Remove useless header `mpscan.h'.
42 * Revision 1.3 2000/06/17 11:42:54 mdw
43 * Moved the Karatsuba macros into a separate file for better sharing.
44 * Fixed some comments. Use an improved technique so that all the
45 * operations are squarings.
47 * Revision 1.2 1999/12/13 15:35:01 mdw
48 * Simplify and improve.
50 * Revision 1.1 1999/12/11 10:57:43 mdw
51 * Karatsuba squaring algorithm.
55 /*----- Header files ------------------------------------------------------*/
61 #include "karatsuba.h"
63 /*----- Tweakables --------------------------------------------------------*/
70 /*----- Main code ---------------------------------------------------------*/
72 /* --- @mpx_ksqr@ --- *
74 * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer
75 * @const mpw *av, *avl@ = pointer to first argument
76 * @mpw *sv, *svl@ = pointer to scratch workspace
80 * Use: Squares a multiprecision integers using something similar to
81 * Karatsuba's multiplication algorithm. This is rather faster
82 * than traditional long multiplication (e.g., @mpx_umul@) on
83 * large numbers, although more expensive on small ones, and
84 * rather simpler than full-blown Karatsuba multiplication.
86 * The destination must be twice as large as the argument. The
87 * scratch space must be twice as large as the argument, plus
88 * the magic number @MPK_SLOP@.
91 void mpx_ksqr(mpw
*dv
, mpw
*dvl
,
92 const mpw
*av
, const mpw
*avl
,
98 /* --- Dispose of easy cases to @mpx_usqr@ --- *
100 * Karatsuba is only a win on large numbers, because of all the
101 * recursiveness and bookkeeping. The recursive calls make a quick check
102 * to see whether to bottom out to @mpx_usqr@ which should help quite a
103 * lot, but sometimes the only way to know is to make sure...
108 if (avl
- av
<= MPK_THRESH
) {
109 mpx_usqr(dv
, dvl
, av
, avl
);
113 /* --- How the algorithm works --- *
115 * The identity for squaring is known to all schoolchildren.
116 * Let %$A = xb + y$%. Then %$A^2 = x^2 b^2 + 2 x y b + y^2$%. Now,
117 * %$(x + y)^2 - x^2 - y^2 = 2 x y$%, which means I only need to do three
121 /* --- First things --- *
123 * Sort out where to break the factor in half.
126 m
= (avl
- av
+ 1) >> 1;
129 assert(((void)"Destination too small for Karatsuba square",
131 assert(((void)"Not enough workspace for Karatsuba square",
134 /* --- Sort out everything --- */
137 mpw
*svm
= sv
+ m
, *svn
= svm
+ m
, *ssv
= svn
+ 4;
141 UADD2(sv
, svm
, av
, avm
, avm
, avl
);
143 mpx_ksqr(tdv
, rdv
+ m
+ 4, sv
, svm
+ 1, ssv
, svl
);
145 mpx_usqr(tdv
, rdv
+ m
+ 4, sv
, svm
+ 1);
148 mpx_ksqr(sv
, ssv
, avm
, avl
, ssv
, svl
);
150 mpx_usqr(sv
, ssv
, avm
, avl
);
151 MPX_COPY(rdv
+ m
+ 1, dvl
, svm
+ 1, svn
);
152 UADD(rdv
, sv
, svm
+ 1);
156 mpx_ksqr(sv
, ssv
, av
, avm
, ssv
, svl
);
158 mpx_usqr(sv
, ssv
, av
, avm
);
159 MPX_COPY(dv
, tdv
, sv
, svm
);
165 /*----- Test rig ----------------------------------------------------------*/
169 #include <mLib/alloc.h>
170 #include <mLib/testrig.h>
172 #define ALLOC(v, vl, sz) do { \
174 mpw *_vv = xmalloc(MPWS(_sz)); \
175 mpw *_vvl = _vv + _sz; \
180 #define LOAD(v, vl, d) do { \
181 const dstr *_d = (d); \
183 ALLOC(_v, _vl, MPW_RQ(_d->len)); \
184 mpx_loadb(_v, _vl, _d->buf, _d->len); \
189 #define MAX(x, y) ((x) > (y) ? (x) : (y))
191 static void dumpmp(const char *msg
, const mpw
*v
, const mpw
*vl
)
196 fprintf(stderr
, " %08lx", (unsigned long)*--vl
);
200 static int usqr(dstr
*v
)
213 ALLOC(s
, sl
, 2 * m
+ 32);
215 mpx_ksqr(d
, dl
, a
, al
, s
, sl
);
216 if (!mpx_ueq(d
, dl
, c
, cl
)) {
217 fprintf(stderr
, "\n*** usqr failed\n");
219 dumpmp("expected", c
, cl
);
220 dumpmp(" result", d
, dl
);
224 free(a
); free(c
); free(d
); free(s
);
228 static test_chunk defs
[] = {
229 { "usqr", usqr
, { &type_hex
, &type_hex
, 0 } },
233 int main(int argc
, char *argv
[])
235 test_run(argc
, argv
, defs
, SRCDIR
"/tests/mpx");
241 /*----- That's all, folks -------------------------------------------------*/